Question: 3. Let A] be an m x 3 matrix, A2 be an m X (n 5) matrix, B1 be an s x r matrix, and

3. Let A] be an m x 3 matrix, A2 be an m X (n 5) matrix, B1 be an s x r matrix, and B; be an (n s) x r matrix. Also suppose that All is an k x 5 matrix, A12 is an R x (n 3) matrix, A21 is an (m k) X 3 matrix, A22 is an (m k) x (n 3) matrix, B11 is an s x I matrix, B12 is an s X (r r) matrix, B21 is an (n s) X 2' matrix, B22 is an (n S) x (r - 2') matrix. Bl (a) (5 points) Prove that (Al A2 ) (B 2 )= A1B1+A2B2. (b) (5 points) Prove that (A11 A12)(Bll BI2)_(A11B11+A12B2I A11B12+AI2BZ2) A21 A22 321 B22 _ A21311+A22321 A2113.12'l'Azzszz Hint: apply Part (a) followed by Question 4 from Tutorial 2

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